arminstraub.com

# A q-analog of Ljunggren's binomial congruence

A q-analog of Ljunggren's binomial congruence
Armin Straub — Discrete Mathematics and Theoretical Computer Science — Special volume for FPSAC 2011 — 2011, Pages 897-902

## Abstract

We prove a $$q$$-analog of a classical binomial congruence due to Ljunggren which states that $\binom{a p}{b p} \equiv \binom{a}{b}$ modulo $$p^3$$ for primes $$p\ge5$$. This congruence subsumes and builds on earlier congruences by Babbage, Wolstenholme and Glaisher for which we recall existing $$q$$-analogs. Our congruence generalizes an earlier result of Clark.

http://dmtcs.episciences.org/2962

@article{qljunggren-2011,
title = {A $q$-analog of {L}junggren's binomial congruence},
}